Notes on Functional Analysis

David K. Zhang
Last Modified 2025-11-22

Definition: Hermite Polynomial, $H_n$

Let $n \in \N$ . The Hermite polynomial $H_n \in \Z[x]$ is defined by the following formula:

H_n(x) \coloneqq (-1)^n e^{x^2} \frac{\dd^n}{\dd x^n} e^{-x^2}